We
have performed a complete moment tensor analysis (Minson and Dreger, 2007) of
the seismic event, which occurred onMonday August 6, 2007 at 08:48:40 UTC, 21 km from Mount Pleasant, Utah.
The purpose of this report is to present our scientific results, making them
available to other researchers working on seismic source determination
problems, and source type identification. In our analysis we used complete,
three-component seismic records recorded by stations operated by the USGS, the University of Utah and EarthScope.
The results of our analysis show that most of the seismic wave energy is
consistent with an underground collapse, however the
cause of the mine collapse is still unknown.

Analysis Method

The
broadband stations from the USGS, the University of Utah
and EarthScope'sUSArray
networks provide excellent azimuthal coverage of the
event. In Figure 1 we show the positions of 16 stations with good signal to
noise levels along with the location of event. We pre-processed the waveform
data by deconvolving the instrument response,
integrating the records to ground displacement, and filtering between 0.02 to
0.10 Hz. The Song et al. (1996) velocity model was used to compute the Green’s
functions used in the moment tensor inversion.

Figure 1. Map with
the event location (yellow star) and stations used (triangles). Data from both
the red and blue stations were used in Figure 2. The red triangles are the
stations closest to the event used for the inversion shown in Figure 3.

For
the moment tensor analysis we assumed a source depth of 1 km, consistent with
the shallow depth reported for this event. As shown in Figure 2 the results using
all 16 stations show a source mechanism with negligible double-couple
radiation. It is dominated by CLVD and implosive isotropic elements. In
contrast a typical earthquake has a moment tensor solution that is dominated by
the double-couple component.

The
total scalar seismic moment in this solution is 1.92x1022 dyne-cm,
corresponding to a moment magnitude (Mw) of 4.2. The long-period records are
very well matched by the model (Figure 2) with an overall variance reduction of
54.1%. The moment tensor solution predicts that the radiation pattern will have
dilational (down) first motion in all directions, or
in other words a “beachball diagram” that is all
white. The nearest stations have better signal to noise levels, and in Figure 3
we show a solution obtained with 6 of the best stations. The two solutions are
in agreement, and as the shown the fit to the data is very good quantified by a
74.1% variance reduction.

See
Appendix A below for an example of a moment tensor inversion of a Mw4.4 earthquake that occurred near Alder Montana.

Figure 2. Moment
tensor solution using 16 regional stations. The observations are solid lines
and the synthetic seismograms are dashed. The P wave radiation pattern, or “beachball diagram” is plotted together with the orientation
of the compressive axis. In the moment tensor mechanism, white areas indicate a
dilatational, or down P-wave first motion. Since this mechanism is all white,
all first arriving P-waves would be expected to be dilatational.

Figure 3. Same
as Figure 2 using six nearby stations with excellent signal to noise levels (red
stations in Figure 1).

To
illustrate why we feel the full moment tensor solution shown in Figures 2 and 3
is correct, we compare a deviatoric moment tensor
inversion in Figure 4. A deviatoric inversion does
not allow for a volumetric source. The fit to the data is visibly worse. While
the transverse component records are fit well in some cases, it is not possible
to fit the transverse and radial/vertical components simultaneously. In fact,
the variance reduction in this case is significantly worse at only 41.8% more
than 30% lower than the preferred solution shown in Figure 3. The P-wave first motion radiation pattern for
the deviatoric solution, its “beachball
diagram”, is substantially different than that in Figures 2 and 3, having a
dominant double-couple component that shows steep dip-slip faulting. This
radiation pattern is not consistent with the observed first motions.

Figure 4. Deviatoric moment tensor solution using the same stations
in Figure 3. Note that the fit of the data is significantly worse than in
Figure 3

P-wave
first motion polarities provide further confirmation of the preferred
mechanism. The P-wave polarities are all down indicating dilational
initial motions. In Figure 5 first-motions picked by Professor Pechmann of the University of Utah are superimposed on the the preferred mechanism from Figure 3 and the deviatoric mechanism (Figure 4). It is clear that the deviatoric moment tensor solution (Figure 5b) does not
agree with the first motion polarities. On the other hand, the preferred full
moment tensor solution (Figure 5a) does satisfy the first motion polarities. To
see an example of first motions for a tectonic earthquake see http://seismo.berkeley.edu/~dreger/fmexample.gif.

The
conclusion drawn from this analysis is that the source mechanism obtained using
shallow (1 km Greens functions) and allowing volume to change at the source
(Figures 2 and 3) is consistent with the collapse of an underground cavity.

Figure 5.
First-motions picked by Professor Pechmann of the University of Utah
are compared to A) the full moment tensor solution (Figure 3) and the B) deviatoric moment tensor solution (Figure 4). Filled
symbols would indicate compressional arrivals (none
were observed), and open circles indicate dilation. The first motion
measurements are obviously more consistent with the preferred inversion result
using the full moment tensor solution which allows volumetric change a the
source.

The
source type plot of Bowers and Hudson (1999) is useful for identifying the
mechanism of the source from a general full moment tensor inversion. In this
type of plot, shown in Figure 6, a measure of the volumetric moment is compared
with the degree of double-couple. Regions of this plot relate to the possible
sources that can be decomposed from a general moment tensor such as a
double-coupled (DC, typical tectonic earthquake), a compensated linear-vector
dipoles (CLVD), dipoles, explosions or implosions, and cracks. The sign on the
x-axis, which passes through the origin, which is a DC defines whether the
major vector dipole of the solution points outward (positive) indicating opening
or inward (negative) indicating closing. Tectonic earthquakes appear close to the
origin in such plots. The solution that we obtained for the Utah event plots in the region defining a
negative crack, or anti-crack, which represents the process of collapse of an
underground cavity (Pechmann et al., 1995; Bowers and Walter, 2002).

Figure 6. Source type
plot based on Bowers and Hudson (1999). In this plot earthquake, explosion and
collapse data from Ford et al. (2007) is compared to the August 6th
event (red star). The August 6th event plots in the general moment
tensor space that defines an closing crack, or collapse. The event is located
well outside the region occupied by tectonic earthquakes.

Analysis
of the sensitivity of the moment tensor solution to source depth indicates that
shallow depths are preferred (Figure 7a). In this analysis 19 stations were
used. The data was processed as described above. Depths of 600m, 800m and 1 km
give similar levels of fit. The slight increase in fit from 2 to 3 km depth is
likely due to the presence of a velocity discontinuity in the structure modeled
used to compute the Green’s functions. Another very interesting result is that the
moment tensor solution remains stable and strongly crack-like over the depth
range from 600m to 5km (Figure 7b). Assumed sources at greater than 5 km depth
become less crack-like, but also remain substantially different from a
double-couple.

Acknowledgements

S.F.'s summer internship at LLNL is supported by the joint
project betweenWilliam R. Walter at LLNL and Doug Dreger at UCB under Department
of Energy BAA contract DE-FC52-06NA27324. This work was performed in part under
the auspices of the U.S. Department of Energy by University of California,
Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.This is LLNL contribution UCRL-TR-233759. We
acknowledge Ralph Falk for his assistance with our P-wave first motion analysis,
and Professors Pankow and Pechmann for providing their first motion data used
in Figure 5.

Appendix A – Example of the Moment Tensor Inversion of the May 8,
2007 Alder Montana
event

On May 8, 2007 a Mw4.4 event
occurred near Alder Montana. This event was well recorded by 149 stations
operated by several organizations (Figure A1). We used the data in the same way
described above to determine the moment tensor of this event. The results shown
in Figure A2 indicate the event is best characterized as a double-couple. The
fit to the deviatoric (non-volumetric) source is 80%.
Allowing a volumetric component increases the fit by 89% and introduces a small
isotropic component. Both the deviatoric and full
moment tensor models provide excellent fit to the data due to the dominant
double-couple component in contrast to the case for the August 6 event.

Figure A1. Location of 8 May
07 event near Alder, MT (red star) and stations used
in the MT analysis (blue diamonds) along with those used in the subset analysis
(white square). All stations ~1000 km from the event are shown (small circles),
where the networks are TA (yellow), BK (orange), IM (red), IU (light orange),
US (green), UW (light blue). Inset, location on continental
US.

Figure A2. a) Data (grey)
and synthetics predicted by the solution using 149 stations (red) and 6
stations with an even azimuthal distribution for a deviatoric solution (green) and full solution (blue). b) Deviatoric focal mechanism where area is scaled by M0,
and source parameters for the 6-station solution c) Deviatoric
and isotropic component (with M0%), for the 6-station solution. c) Deviatoric focal mechanism and isotropic component for the
149-station solution. VR in title is the % variance reduction, a goodness of
fit measure.